The engine ECU executes a program including the step of detecting an engine coolant temperature, the step of detecting an engine speed and an engine load, the step of estimating a temperature at a tip end of an in-cylinder injector based on the engine coolant temperature, the engine speed and the engine load, and, when the temperature at the tip end is greater than a guaranteed temperature, the step of calculating a drive duty of a high-pressure fuel pump that ensures a decrease of the temperature at the tip end of the in-cylinder injector to the guaranteed temperature, and the step of controlling the high-pressure fuel pump using the drive duty.